Background Modeling forms a central module in systems using Computer Vision to detect events of interest in a video stream. Most current methods use only the intensity observed at a pixel. Such a model is reasonable when the background is stationary. However, these methods deteriorate in their discrimination power when the background is dynamic. Examples of these include ocean waves, waving trees, rain, moving clouds, and camouflaged objects that are camouflaged such that they are of similar color as the background of the object.
A Hough Transform is a method for detecting straight lines and curves on gray level images. For line detection, the equation of a line can be expressed as ρ=x cos(θ)+y sin(θ), where θ and ρ are the line orientation and the line distance from origin to the line, respectively. A line is therefore, completely specified by a parameter pair (θ,ρ). For straight line detection, the Hough Transform maps each pixel (x,y) from the image space into a parameter space of (θ,ρ), where contributions from each feature point to each possible set of (θ,ρ), which are accrued. For this purpose, the parameter space is divided into cells with each cell corresponding to a pair of quantized (θ,ρ). A multi-dimensional accumulator array is often used to represent the quantized space. For each feature point, all the parameters associated with the point are estimated, the corresponding cells of the accumulator are incremented accordingly. This is repeated for all feature points. Lines are found by searching the accumulator array for peaks. The peaks correspond to the parameters of the most likely lines.
The standard Hough Transform adopts a “top hat” strategy to compute the contribution of each point to a hypothesized line. Specifically, the scheme assumes all feature points located within a close range of the hypothesized line contribute equally to the line. The accumulator is, therefore, incremented by a unit for those feature points. This scheme is inadequate in that data points are not all equally reliable. This means that line parameters derived from each feature point may carry different uncertainties due to the following reasons. Most Hough Transform techniques employ certain techniques for estimating the orientation of feature points (edgels) to restrict the ranges of values of θ a pixel may vote for. The estimation of the orientation of each edge pixel is often uncertain due to: 1) image noise, for example, positional errors from quantization and sensor errors, 2) small neighborhood associated with the edge detection procedure and the inherent uncertainty with the procedure, and 3) the parametric representation used to define a line. Therefore, feature points vary in uncertainties and should not be treated equally.
Previous efforts in algorithm improvement to Hough Transforms focused on improving the computational efficiency of the Hough Transform, that is, speed and memory. Early efforts in this aspect concentrated on reducing the number of bins used for tessellating the parameter space. Many proposed techniques drew on some form of coarse-to-fine search strategy resulting in a dramatic reduction of cells.
Recent efforts have been focusing on sampling the feature points. The idea is to use only a subset of image features. These efforts give rise to different probabilistic, also called randomized, Hough Transform techniques which increase the computational efficiency and decrease memory usage by means of sampling the image feature space.
Therefore, a need exists for a unified framework that utilizes the uncertainty of transformed data for peak detection and clustering in feature space. A further need exists for a method for background modeling that is able to account for dynamic backgrounds that change according to a certain pattern. A still further need exists to analyze Hough Transforms that are built with uncertainty and a need exists for video segmentation in invariant color spaces.